In this work, a hybrid finite element formulation is presented to predict the flutter boundaries of circular cylindrical shells made of functionally graded (FG) materials. The development is based on a combination of linear Sanders thin shell theory and the classic finite element method. Material properties are temperature dependent and graded in the shell thickness direction according to a simple power law distribution in terms of volume fractions of constituents. The temperature field is assumed to be uniform over the shell surface and along the shell thickness. First-order piston theory is applied to account for supersonic aerodynamic pressure. The effects of temperature rise and shell internal pressure on the flutter boundaries of a FG circular cylindrical shell for different values of power law index are investigated. The present study shows efficient and reliable results that can be applied to aeroelastic design and analysis of shells of revolution in aerospace vehicles.

References

References
1.
Reddy
,
J. N.
, and
Chin
,
C. D.
,
1998
, “
Thermomechanical Analysis of Functionally Graded Cylinders and Plates
,”
J. Therm. Stress
,
21
(
6
), pp.
593
626
.10.1080/01495739808956165
2.
Suresh
,
S.
, and
Mortensen
,
A.
,
1998
,
Fundamentals of Functionally Graded Materials: Processing and Thermo-Mechanical Behavior of Graded Metals and Metal Ceramic Composites
, IOM Communications Ltd.,
London, UK
.
3.
Haddadpour
,
H.
,
Mahmoudkhani
,
S.
, and
Navazi
,
H. M.
,
2007
, “
Free Vibration Analysis of Functionally Graded Cylindrical Shells Including Thermal Effects
,”
Thin-Walled Struct.
,
45
(
6
), pp.
591
599
.10.1016/j.tws.2007.04.007
4.
Kadoli
,
R.
, and
Ganesan
,
N.
,
2006
, “
Buckling and Free Vibration Analysis of Functionally Graded Cylindrical Shells Subjected to a Temperature-Specified Boundary Condition
,”
J. Sound Vib.
,
289
(
3
), pp.
450
480
.10.1016/j.jsv.2005.02.034
5.
Pradhan
,
S. C.
,
Loy
,
C. T.
,
Lam
,
K. Y.
, and
Reddy
,
J. N.
,
2000
, “
Vibration Characteristics of Functionally Graded Cylindrical Shells Under Various Boundary Condition
,”
Appl. Acoust.
,
61
(
1
), pp.
111
129
.10.1016/S0003-682X(99)00063-8
6.
Wu
,
L.
,
Jiang
,
Z.
, and
Liu
,
J.
,
2005
, “
Thermoelastic Stability of Functionally Graded Cylindrical Shells
,”
J. Compos. Struct.
,
70
(
1
), pp.
60
68
.10.1016/j.compstruct.2004.08.012
7.
Shen
,
H.-S.
, and
Noda
,
N.
,
2005
, “
Postbuckling of FGM Cylindrical Shells Under Combined Axial and Radial Mechanical Loads in Thermal Environments
,”
Int. J. Solids Struct.
,
42
(
16
), pp.
4641
4662
.10.1016/j.ijsolstr.2005.02.005
8.
Mirzavand
,
B.
, and
Eslami
,
M. R.
,
2006
, “
Thermal Buckling of Imperfection Functionally Graded Cylindrical Shells Based on the Wan-Donnel Model
,”
J. Therm. Stresses
,
29
(
1
), pp.
37
55
.10.1080/01495730500257409
9.
Prakash
,
T.
, and
Ganapathi
,
M.
,
2006
, “
Supersonic Flutter Characteristics of Functionally Graded Panels Including Thermal Effects
,”
J. Compos. Struct.
,
72
(
1
), pp.
10
18
.10.1016/j.compstruct.2004.10.007
10.
Navazi
,
H. M.
, and
Haddadpour
,
H.
,
2007
, “
Aero-Thermoelastic Stability of Functionally Graded Plates
,”
J. Compos. Struct.
,
80
(
4
), pp.
580
587
.10.1016/j.compstruct.2006.07.014
11.
Ibrahim
,
H. H.
,
Yoo
,
H. H.
, and
Lee
,
K.-S.
,
2009
, “
Supersonic Flutter of Functionally Graded Panels Subjected to Acoustic and Thermal Loads
,”
J. Aircr.
,
46
(
2
), pp.
593
600
.10.2514/1.39085
12.
Haddadpour
,
H.
,
Navazi
,
H. M.
, and
Shadmehri
,
F.
,
2007
, “
Nonlinear Oscillation of a Fluttering Functionally Graded Plate
,”
J. Compos. Struct.
,
79
(
2
), pp.
242
250
.10.1016/j.compstruct.2006.01.006
13.
Haddadpour
,
H.
,
Mahmoudkhani
,
S.
, and
Navazi
,
H. M.
,
2008
, “
Supersonic Flutter Prediction of Functionally Graded Cylindrical Shells
,”
J. Compos. Struct.
,
83
(
4
), pp.
391
398
.10.1016/j.compstruct.2007.05.011
14.
Mahmoudkhani
,
S.
,
Haddadpour
,
H.
, and
Navazi
H. M.
,
2010
, “
Supersonic Flutter Prediction of Functionally Graded Conical Shell
,”
J. Compos. Struct.
,
92
(
2
), pp.
377
386
.10.1016/j.compstruct.2009.08.018
15.
Sabri
,
F.
, and
Lakis
,
A. A.
,
2010
, “
Finite Element Method Applied to Supersonic Flutter of Circular Cylindrical Shells
,”
AIAA J.
,
48
(
1
), pp.
73
81
.10.2514/1.39580
16.
Sanders
,
J. L.
, Jr.
,
1959
, “
An Improved First-Approximation Theory for Thin Shell
,” NASA Technical Report No. R-24.
17.
Rumhaar
,
H.
,
1963
The Accuracy of Linear Piston Theory When Applied to Cylindrical Shells
,”
AIAA J.
,
1
(
6
), pp.
1448
1449
.10.2514/3.1832
18.
Sabri
,
F.
, and
Lakis
,
A. A.
2011
, “
Effects of Sloshing on Flutter Prediction of Partially Liquid-Filled Circular Cylindrical Shells
,”
J. Aircr.
,
48
(
6
), pp.
1829
1839
.10.2514/1.C031071
You do not currently have access to this content.